- Turkish Journal of Mathematics
- Vol: 37 Issue: 6
- On the Pollard decomposition method applied to some Jacobi--Sobolev expansions
On the Pollard decomposition method applied to some Jacobi--Sobolev expansions
Authors : Francisco Marcellán, Yamilet Quintana, Alejandro Urieles
Pages : 934-948
Doi:10.3906/mat-1208-29
View : 9 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :Let {qn(a,b)}n \geq 0 be the sequence of polynomials orthonormal with respect to the Sobolev inner product \langle f,g\rangleS:=\int-11f(x)g(x)w(a,b)(x)dx+\int-11f'(x)g'(x)w(a+1,b+1)(x)dx, where w(a,b)(x)=(1-x)a(1+x)b, x\in [-1,1] and a,b>-1. This paper explores the convergence in the W1,p\left((-1,1), (w(a,b),w(a+1,b+1))\right) norm of the Fourier expansion in terms of {qn(a,b)}n\geq 0 with 1< pKeywords : Sobolev orthogonal polynomials, weighted Sobolev spaces, Fourier expansions, Sobolev--Fourier expansions